Evolution of inelastic plane curves
type: Item
instance of: scholarly article
title: Evolution of inelastic plane curves
zbMATH Open document ID: 0964.53006
DOI: 10.1016/S0893-9659(99)00088-9
published in: Applied Mathematics Letters
publication date: 2001-05-06T00:00:00Z
review text: This short note discusses geometric flows for planar curves, of the form \(\partial F/\partial t = f T + g N\), which are `inelastic' or locally arclength-preserving; \(f\) and \(g\) are functions of the curvature \(\kappa\). The main results are that for such flows \(\partial f/\partial s= g\kappa\), and \(\partial \kappa/\partial t = \partial/\partial s(f\kappa +\partial g/\partial s)\). These, however, are easy consequences of formulas that appeared in papers by \textit{J. Langer} and \textit{D. Singer} [J. Differ. Geom. 20, 1-22 (1984; Zbl 0554.53013)] and \textit{J. Langer} and \textit{R. Perline} [J. Nonlinear Sci. 1, 71-93 (1991; Zbl 0795.35115)] -- and elsewhere, no doubt. The note concludes with three short examples.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 1369313
zbMATH Keywords: plane curve
zbMATH Keywords: geometric evolution equation
author: Do Yong Kwon
author: Frank Chongwoo Park
reviewed by: Thomas A. Ivey
MaRDI profile type: Publication
cites work: Design of developable surfaces using duality between plane and point geometries
cites work: The heat equation shrinking convex plane curves
cites work: The heat equation shrinks embedded plane curves to round points
cites work: Q4091004
description: scientific article; zbMATH DE number 1369313